I checked the post #1 of this thread and cannot find any info @ the present about the important SELinux security status under What is working and What is not working.
So can you guys or ChronoMonochrome check in > Settings > Security and Privacy ...
Thanks for your efforts, ROM is working fine with great performance but ROM boots with selinux as permissive not enforcing.
Try turning off the S3, wait 10 seconds & turn back on.
If you still don't have cellular network data try the SIM in an other phone as it may be a carrier provisioning problem.
If data works in an other phone but not with the SIM back in y...